2019/10/31 by Tibor Rakovszky, Pablo Sala, Ruben Verresen +2 · 182 citations
Mathematics · Physics and Astronomy · #Dipole #Eigenvalues and eigenvectors #Ergodic theory #Excited state #Hilbert space #Integrable system #Mathematical physics #Mathematics #Model Reduction and Neural Networks #Opinion Dynamics and Social Influence #Physics #Pure mathematics #Quantum #Quantum many-body systems #Quantum mechanics #cond-mat.stat-mech #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevb.101.125126
published in Physical review. B./Physical review. B 101(12) (American Physical Society) · Close to published version
openalex publication_date 2020/03/25 · arxiv created 2020/05/12 · arxiv updated 2020/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Certain disorder-free Hamiltonians are nonergodic due to a s\phantom\rule00ext\phantom\rule00exr\phantom\rule00exo\phantom\rule00exn\phantom\rule00exg f\phantom\rule00exr\phantom\rule00exa\phantom\rule00exg\phantom\rule00exm\phantom\rule00exe\phantom\rule00exn\phantom\rule00ext\phantom\rule00exa\phantom\rule00ext\phantom\rule00exi\phantom\rule00exo\phantom\rule00exn of the Hilbert space. Here, the authors introduce the notion of ``statistically localized integrals of motion'' (SLIOM) to characterize these systems. Despite SLIOMs being nonlocal operators, they become spatially localized to subextensive regions when their expectation value is taken in typical states. These can also result in statistically localized s\phantom\rule00ext\phantom\rule00exr\phantom\rule00exo\phantom\rule00exn\phantom\rule00exg z\phantom\rule00exe\phantom\rule00exr\phantom\rule00exo m\phantom\rule00exo\phantom\rule00exd\phantom\rule00exe\phantom\rule00exs, leading to topological string order for certain highly excited eigenstates as well as infinitely long-lived edge magnetization along with a thermalizing bulk.